Lee weights of cyclic self-dual codes over Galois rings of characteristic p2

Boran Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We completely determine the minimum Lee weights of cyclic self-dual codes over a Galois ring GR(p2,m) of length pk, where m and k are positive integers and p is a prime number. We obtain all cyclic self-dual codes over GR(22,1)≅Z4 of lengths 16 and 32 with their Lee weight enumerators. We also find cyclic self-dual codes over GR(32,1)≅Z9 (respectively, GR(32,2)) of lengths up to 27 (respectively, 9). Most of the cyclic self-dual codes we found are extremal with respect to the Lee weights.

Original languageEnglish
Pages (from-to)107-130
Number of pages24
JournalFinite Fields and their Applications
Volume45
DOIs
StatePublished - 1 May 2017

Keywords

  • Cyclic code
  • Extremal code
  • Galois ring
  • Minimum Lee weight
  • Self-dual code

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